Hi axelator
If what you have is really medial tibial stress syndrome - and it can be misdiagnosed for other problems, then you are actually doing all the right things in getting your leg muscles in better condition. It may be just that skipping, running and sprinting is still overloading the insertions of the muscles involved too much. MTSS is really an overuse injury so you can easily make it worse as you increase your activity.
The pathology can be a bit complex but it includes tendon and fascia problems where the soleus (deep layer of the calf muscle) and the flexor digitorum longus (muscle that bends the toes) attach high up in the shin. the tendons can actually pull on the periosteum - the fibrous tissue that covers the bones and this can be what gives you the pain. the periosteum and the tendons do respond to graded conditioning (ie enough stress to stimulate strengthening of the tissue but not too much to overload and irritate the tissue and make matters worse) However these tissues take much longer to respond than muscle to conditioning and you will just have to be patient and persevere slowly. Muscle has a very good blood supply and is a very responsive body tissue while tendon, fascia and perisoteum have a much poorer blood supply and take much longer to adapt. There is an art to stimulating the tissues just enough to get a good result but not overtraining that will just set you back.
Further strengthening of the ankle and foot muscles including eccentric training (particularly but not limited to the calf muscles) are good. You can gradually add jogging on sprung surface or thin high density mat just working within what is comfortable and slowly increasing the dosage. Then you could add in skipping but keep on a sprung surface. the principle is just gradually increase the stress, always keeping to what is comfortable and so you are not getting delayed soreness. You won't achieve anything by overloading these tissues.
Other things to have checked are your shoes - are they providing adequate support. And you need to be checked for varus of the hind foot and overpronation as these foot problems go hand in hand with MTSS